Implementation of 1D+4D-Var Assimilation of Precipitation ...

487

Implementation of 1D+4D-VarAssimilation of Precipitation

Affected Microwave Radiances atECMWF, Part I: 1D-Var

Peter Bauer1, Philippe Lopez1, AngelaBenedetti1, Deborah Salmond1 and

Emmanuel Moreau 2

Research Department

1European Centre for Medium-Range Weather Forecasts, UK2NOVIMET, France

Accepted for publication in Quart. J. Roy. Meteor. Soc.

February 2006

Series: ECMWF Technical Memoranda

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1D+4D-VarAssimilationof PrecipitationAffectedMicrowaveRadiances:1D-Var

Abstract

This paperpresentsthe operationalimplementationof a 1D+4D-Var assimilationsystemof rain affectedsatelliteobservationsat ECMWF. Thefirst partdescribesthemethodologyandperformanceanalysisof the1D-Var retrieval schemein cloudsandprecipitationthatusesSSM/I microwave radianceobservationsfortheestimationof total columnwatervapor. Thesecondpartshowstheglobalandlong-termimpactof theseobservationson bothmodel4D-Varanalysesandmedium-rangeforecasts.

The1D-Var schemeemploys a complex observationoperatorthat consistsof linearizedmoistphysicspa-rameterizationschemesanda multiple scatteringradiative transfermodel.Theobservationoperatorshowsa ratherlinearbehavior in mostsituationsexceptin thepresenceof very intenseprecipitationsuggestingapossibleuseevenfor a directassimilationof radiancesin 4D-Var. A biascorrectionandobservationerrorestimationmethodwereimplementedandindicatestableerrorbehavior. The1D-Varalgorithmqualitycon-trol shows the largestfailure numberin areaswith mostly frozenprecipitationwherethe SSM/I channelshave little sensitivity to changesin hydrometeorcontents.From testanalyseson a global scale,a smallmoistureincreasewas computedthat was greatestin dry subtropicalareas. Large-scaleand convectiveprecipitationwereincreasedsimilarly but showed a significantlydifferentgeographicaldistribution. Thelarge-scaleprecipitationschemehasastrongersensitivity to moisturechangesandthereforemoistureincre-mentsmainly affect stratiformprecipitationdistributions. While the globalmeanmoisturefields areonlyweaklyaffectedby theassimilationof rain affectedobservations,theimpacton local systemsmaybequitelarge.Theforecastof synopticsystemdevelopmentthroughthe4D-Varanalysiscanbesignificant.

1 Intr oduction

Thefocusof this two-partpaperis theimplementationof a rainassimilationframework in theglobalmodelingsystemat ECMWF. This purposeprescribesalreadythechoiceof methodologiesto beemployedandthedefi-nition of someconstraintsgivenby theexistingmodelconfiguration.Firstly, ECMWFoperatesanincrementalformulationof a four-dimensionalvariational(4D-Var) dataassimilationsystemwith four analysesper day,namelytwo 12-hourassimilationwindow andtwo 6-hourassimilationwindow ones.Theformerproducethebackgroundfields for the latter while the latter producetwo 10-dayforecastsinitialized at 00 and12 UTC,respectively. A vastsetof observationsareassimilatedof whichabout98%originatefrom satellitedata.Thesearealmostexclusively screenedfor cloud andrain contaminationexcept for thosesounderchannelsthat arenotsensitive to themid to lower troposphere.Thisproducesananalysisbiasin termsof datacoveragetowardscloud-freeareasthatarethereforemuchmorestronglyconstrainedby observationsthancloudyandrain affectregions.

Theassimilationof rainfall observationsin numericalweatherprediction(NWP) modelshasbeencoveredinvariousresearchstudiesover the last20 years.Themostapparentissueswhendealingwith this new typeofobservationsare(1) thechoiceof rain-relatedobservationtreatmentandtheestimationof its errorcharacteris-tics (e.g.Errico et al. 2000),(2) theinteractionwith themoistphysicsparameterizationschemesin themodel,in particulartheir possiblynon-linearresponseto constraintsintroducedby theobservations(e.g. Fillion andErrico1997),and(3) theresponseof themodeldynamicsthatis thetrade-off betweenthedesiredimprovementof moisturedistributions throughmodificationof divergencefields andthe unwantedeffect of, for example,gravity wave excitation by unbalancinglocal dynamics(e.g. Fillion 2002). Detailsof theseissuesthat arerelatedto the variationalassimilationof rain observationsin the presentmodelconfigurationwith respecttootherstudieswill bepresentedin partII of thispaper(Baueret al. 2006a).

At ECMWF, new satelliteobservationshave beenassimilatedthroughone-dimensionalvariational(1D-Var)retrievals of intermediateparametersbeforea direct assimilationof electromagneticradianceswasattempted(e.g. Eyre et al. 1993,Phalippou1996). The advantageof this choiceis the bettercontrol of a non-linearresponseof the observation operatorto changesin the atmosphericstateas well as the additional level of

TechnicalMemorandumNo. 487 1


qualitycontrolbeforedatais passedon to the4D-Var system.For cloudobservations,1D-Var retrieval studieshave beencarriedout (Chevallier et al. 2002,DeblondeandEnglish2003)that provide a lot of insight intoobservation operatorandminimization performancefrom flexible sensitivity testingthat is basedon globalmodelstatistics.For rain observationsMarecalandMahfouf (2000,2002)developeda similar approachusingTropical Rainfall MeasuringMission (TRMM) Microwave Imager(TMI) basedsurfacerain rateestimates.Theirwork wascrucialfor all furtherstudiesatECMWFbecausemostof theissueslistedabovewerediscussed.

Chevallier andBauer(2003)showedthatmicrowave radiancesthataresimulatedusingglobalmodelfieldsarequite realistic. Later, the direct useof microwave radiancesinsteadof rain rateobservationswasestablishedin the variationalretrieval method(Moreauet al. 2002). A direct comparisonof radiancewith rain rateob-servationsin the1D-Var (Moreauet al. 2003)revealsthat thechoiceof radiancesmainly servesto avoid thedependenceon sensor-specificretrieval algorithmsandto simplify the ratheruncertainerror estimation(e.g.Baueret al. 2002). Thedevelopmentsthat leadto the implementationwhich becameoperationalat ECMWFon June28, 2005,were(1) theimplementationof the1D-Var radianceassimilationin modelgrid-pointspacethatis activatedateachtimestep(currently15minutes)in theassimilationwindow, (2) theimprovementof theobservation operatorincluding its tangent-linearandadjointversions,(3) extensive testingof its performancewith globalandlong-termdata,(4) theimplementationof qualitycontrol,biascorrectionandobservationerrorformulation,(5) extensive testingof theimpactof theassimilationon globalmodelanalysesandforecasts.

This paperconsistsof two parts,the first beingpresentedhereand the secondshowing the impact of totalcolumnwatervapour(TCWV) pseudo-observations that werederived from the 1D-Var retrieval on the 4D-Var analysesandforecasts.Section2 of this paperintroducesthe 1D-Var set-upandpresentsthe combinedmoistphysics-radiative transferobservationoperator. Thelinearity of theoperatoris investigatedusingrealis-tic perturbationsthatmayleadto conclusionsregardinga potentialdirectassimilationof rain affectedpassivemicrowave observationsin the 4D-Var analysis. Section3 describesthe dataprocessingincluding the biascorrectionschemeandevaluatestheperformanceof the1D-VaralgorithminsidetheECMWFanalysissystem.Problematiccasesareidentifiedin which convergenceproblemsoccuror unrealisticretrieval resultsarepro-ducedandthathaveto beenscreenedout. Thepaperis concludedby adiscussionof thedevelopedmethodologybasedon theshown results.

2 Algorithm

2.1 Optimum estimation

Theassimilationof radiancedatain precipitationrepresentsaninversionproblemthatis not fully constrained.If, for example,SpecialSensorMicrowave / Imager(SSM/I) or TMI-type microwave channelsareavailableasobservations,they representonly 2-3 statisticallyindependentmeasurements(e.g. Bauer2001).Therefore,large weight is put on the ’a priori’ constraintsthatarethebackgroundprofilesof temperatureandmoisture,their error structure,and the observation operatorthat may comprisemoist physicsparameterizationsandaradiative transfermodel.However, thefeasibilityof avariationalframework usingthisset-uphasbeendemon-stratedandtestedwith variousradiometerchannelcombinations(Moreauet al. 2002,2003).

In thefollowing, theobservationsalwaysreferto radiancesmeasuredby theSSM/I thatareexpressedasblack-bodyequivalentbrightnesstemperatures(TB’s) in unitsof degreesKelvin (K). TheSSM/I hassevenchannelswith dualpolarizationmeasurementsat 19.35,37.0and85.5GHz, respectively, andverticalpolarizationmea-surementsat 22.235GHz. Hereafter, thechannelswill bereferredto as19v, 19h,22v, 37v, 37h,85v, and85hto identify measurementfrequency andpolarizationin a simpleway. Thelogical flow of the1D -Var retrievalis shown in Figure1.

2 TechnicalMemorandumNo. 487


�� Observations:yo�

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Figure1: Logical flowof SSM/Iradianceprocessingand1D-Var retrieval.

In thevariationalretrieval (e.g. Rodgers2000),theoptimumestimateof a statevector, x, is obtainedusinganobservationvector(TB’s),yo, plusadditionala priori information.Dueto theuncertaintiesassociatedwith thebackgroundstate,observationsandtheobservationoperator, H (thatmapsgeophysicalspaceontoobservationspace),the relationbetweenstateandobservation spaceis usuallydescribedby probabilitydensityfunctions(pdf’s). Applying Bayes’theoremandassumingthat theerrorsof backgroundstate,xb, andobservationsareuncorrelatedandhave a Gaussianshape,the inversionproblemcanbeformalizedby theminimizationof thewell-known costfunction,J:

J x � � 12 x xb � TB � 1 x xb �� 1

2

�yo H x �� TR � 1 � yo H x �� (1)

with backgrounderror covariancematrix B and observation error covariancematrix R. The latter includesthe modelingerror of operatorH that is likely to be larger than the instrumentnoiseof the SSM/I that istypically between0.5-0.8K. Theissueof thespecificationof errorsandtheir Gaussiandistribution shapewillbediscussedin Section3b.

Thenon-linearityof H is not necessarilyanissuein this implementationbecausethevariationalretrieval mayemploy a non-linearminimizationprocedure.This representsan advantagefor large differences(first-guessdepartures)betweenyo andH xb � . Thelinearityof theentireobservationoperatoris investigatedin Section2bandthedeparturestatisticsareanalyzedin Section3a,respectively.

In our application,the control vectorx containsvertical profilesof temperatureandspecifichumidity on 60modellevels,henceits dimensionof 120 in thecurrentECMWF modelversion. Theminimizationof Equa-tion (1) requiresthegradientof J x � :

∇J x �� B � 1 x xb �� HTR � 1 �H x � yo � (2)

whereHT is the adjoint of the observation operator. The quasi-Newtonian(M1QN3) softwaredevelopedby(GilbertandLemarechal1989)is usedto performtheminimization.

Theminimizationis pre-conditionedfor convergenceimprovementby decomposingB � EΛET whereE is thematrixof eigenvectorsof B andΛ is amatrixwhosediagonalcontainstheeigenvaluesof B. Thestatevectorx



is transformedto κ with forwardandbackwardtransformations:

κ � Λ � 1� 2ET x xb � (3)

x � xb � EΛ1� 2κ

sothatthecostfunctiongradientbecomes:

∇J κ �� κ � Λ1� 2ETHTR � 1 �H x � yo � (4)

Theabovetransformationis appliedbeforeandaftertheminimization,respectively, andis justifiedby theratherdifferentmagnitudesof departuresandbackgrounderrorsof theseparameters.

2.2 Observation operator

Theobservationoperatorcontainsmoistphysicsparameterizationschemesanda multiple-scatteringradiativetransfermodel. Themoistphysicsparameterizationsconsistof a large-scalecondensationscheme(TompkinsandJaniskova 2004)anda convectionscheme(LopezandMoreau2005). Both representmodelsthat aim ata similar performanceof the forward modelsasthe non-linearmoist physicsparameterizationsemployed atECMWF (Tiedtke 1989,1993). However, they representmodelversionwhosesensitivity to perturbationsoftheinputparametersis morelinearthanthatof theTiedtke-parameterizations. Thisproducesamorecontrolledbehavior in the minimization and avoids excessive incrementsthat may causeconvergenceproblems. Themultiple-scatteringradiative transfermodelis partof theRTTOV softwarepackage(e.g.Saunderset al. 2005)thathasbeenextensively testedfor dataassimilationpurposesby Baueretal. (2006b).

Theconvectionschemerepresentssubgrid-scaleprocessesandtreatsseveralconvectiontypes,namelyshallow,mid-level anddeepconvection, in a unified way. In contrastto previous modelsemployed at ECMWF, thetangent-linearandadjointmodelsaccountfor perturbationsof all convectivequantitiessuchasconvective massflux, updraughtcharacteristicsandprecipitationflux. Thelarge-scalecondensationschemeusestheconvectivedetrainmentprescribedby theconvectionmodelwith asimilarprecipitationgenerationformulation.Thecloudschemeappliesastatisticalmethodfor thedescriptionof subgrid-scalecloudfluctuationsaffectingcloudcoverandcloudwater. Subgrid-scalevariability of humidity is usedto provideanimprovedmodelingof precipitationevaporation.Theradiative transfermodelappliestheDelta-Eddingtonapproximationto radiative transferthatis widely consideredsufficiently accurateat microwave frequencies(Smith et al. 2002). The output fromthemoistphysicsparameterizations,i.e., cloudcover andprecipitationfluxesareusedto computecloudlayeropticalpropertiesbasedonpre-calculatedlook-uptables.

Theobservation operatorrequiresmoreinput variablesthanthosecontainedin thecontrol vectorx. The fullsetof parametersis referredto asthestatevector(seeTable1). It containstheprofilesof specifichumidityandtemperature(which representthecontrol vector)aswell astheir tendenciesplussurfacefields. Thesearethelatentandsensibleheatflux, thezonalandmeridionalcomponentsof wind stressand10-meterwindspeed,skintemperatureandpressure,2-metertemperature,2-meterspecifichumidity and2-meterdew-point temperature.Themoistphysicsparameterizationsproduceprofilesof fractionalcloud cover, cloud liquid andice wateraswell asliquid andfrozenprecipitation.The hydrometeorprofilesrepresentthe input to the radiative transfermodeltogetherwith the10-meterwindspeed,theskin temperatureandbothtemperatureandmoistureprofiles.Notethatonly thecontrolvectoris containedin thecost-functionin Equation(1) while statevectorcomponentsmaybeaffectedby changesin thecontrolvectorduringminimizationbut donotaffectthecost-functiondirectly.

The accuracy of the observation operatorcannot be directly determinedbecausethe requiredin situ obser-vationsof all parametersarenot available. The relative accuracy of the moist physicsparameterizationsis



Table1: Input (I) andoutput(O) parametersof observationoperator components.Convection Large-scalecondensation Radiative Transfer

Profiles:Temperature I I ISpecifichumidity I I ITemperaturetendency I ISpecifichumidity tendency I IDetrainedconvective cloudwater O ICloudwatercontent O O ICloudice content O O ICloudcover fraction O ILiquid precipitationflux (rain) O O IFrozenprecipitationflux (snow) O O ISurfacefields:Latentheatflux ISensibleheatflux IWind stress(zonal,meridional) I10-meterwind speed(zonal,meridional) I2-metertemperature I2-meterdew-point temperature I2-meterspecifichumidity IPressure I I ISkin temperature I

evaluatedfrom comparisonto thenon-linearECMWF cloudandconvectionschemes.Thosehave beenevalu-atedin theframework of globalmodelintercomparisonstudiesundertheauspicesof, for example,theWMOWorking Groupon NumericalExperimentation(WGNE) or the Global Energy andWaterCyle Experiment(GEWEX) CloudSystemStudy(GCSS).Theradiative transfermodel’s mainsourcesof erroraretheapproxi-mationof radiationpropagationthroughbrokencloudsandtheassumptionsmadefor calculatingparticlesinglescatteringproperties(e.g. for particlesizedistributions;Baueret al. 2006b). As a generallyapplicableerrorestimatefor dataassimilation,anindirectmethodwasapplied(seeSection3b).

Theassimilationof rain-affectedmicrowaveradiancesis new andthereforelittle workhasbeenpublishedontheperformanceof thecombinedmoistphysics- radiative transferobservationoperator. Apart from computationalefficiency, themostfundamentalquestionis how linearly theobservationoperatorbehaves.This is particularlyimportantif theoperatoris appliedwithin incrementalvariationalassimilationsystems.Thetestof theadjointcodeis straightforwardbecauseit only relieson a numericalcheckusingbothtangent-linearandadjointcodeversions.Theinvolvedadjointtestshave beencarriedout successfullyandwill notbereproducedhere.

The linearity testsare basedon comparingthe output of the tangent-linearmodel with thosefrom finite-differencecalculationsusingtheforwardmodel.For exampletheratio:

F � H x � λδx � H x �λH δx � (5)

maybeusedasa linearity measurein which δx representsthe initial perturbationof thecontrolvectorandλis ascalingfactor. In thelinearcase,scalingof theoutputof thetangent-linearmodelshouldproducethesameresultasthescalingof theinput to theforwardmodel.

Thescalingfactor, λ , usuallyspansseveralordersof magnitudeto sampleall possibleperturbationsizes.The



δx shouldberealisticbecause,theoretically, δx couldbechosentoosmallsothatevenrathernon-linearmodelsshow a nearlylinearperformance.Errico andRaeder(1999)investigatedthe limitationsof thetangent-linearapproximationto moist physicsparameterizationsand pointedout the importanceof adequatetestingwithrealisticperturbationsvs. infinitesimalones. In variationalanalyses,theperturbationsareof theorderof themodeluncertaintieswhicharesimilar to thefirst-guessdepartures.

In ourcase,theanalysisminusfirst-guessdeparturesfrom the1D-Varanalysisserve thispurposebecausetheydefinetheimprovementof thefirst-guessstatethatwasachievedby constrainingtheretrieval with observationsgiventhedefinedmodelandobservationerrors,respectively. Therefore:

δx � xa xb (6)

which is scaledwith λ rangingfrom 10� 10 to 1 with incrementsof 102. The linearity of the moist physicsparameterizationscomponentandthetotal observationoperatorcanbetestedseparately. Sincex is thecontrolvectorit containsprofilesof temperatureandspecifichumidity. If only themoistphysicsparameterizationsaretestedtheoutputof H x � consistsof profilesof hydrometeorsandcloudcover. F canthenbe displayedasafunctionof therespective output,i.e.,hydrometeorcontentsor SSM/I channelradiances.

Figures2-4show histogramsof log10 � 1 F � from 8,290profilesdistributedoverglobaloceansfrom two modelanalysesat 00 and12UTC on December31,2004.Ideally, F shouldapproachzeroandthehistogramsshouldshow themajority of thedataat very low values.If log10 � 1 F �� 0, a decentlylinearregimeis achieved,andfor example,at log10 � 1 F � � 1, F would lie between0.9 and1.1 that is a 10%disagreementbetweenthefinite-differenceandthetangent-linearcalculations.

For rain (Figure2), thedistribution doesnot show muchsensitivity to altitudewhich is becauseprecipitationis computedwith a diagnosticschemethat immediatelyrainsout the hydrometeorsoncethey have formed.For very small λ , the resultsdeterioratedueto numericallimitations. For large λ , the resultsdeteriorateaswell becausethe largerperturbationsproducestrongernon-linearities.An optimumstatecanbeidentifiedforλ � 10� 6 thatproducesthehighestconcentrationof casesnear 7. Thereareclearlytwo regimesvisible thatmarknearlylinearandrathernon-linearsituationswhichcorrespondto deeperlayersandheavier precipitation(rain flux greaterthan10� 3kg m� 2s� 1). This regime is almostindependentof λ becausefor intensesystems,largesensitivities to smallperturbationsmayexist. For frozenprecipitation(Figure3) thereis astrongaltitudedependence.For higheraltitudesthe linearity improvesdueto lower snow contents.Above 550 hPa (modellevel 40) snow mainlyoccursin themoreintensesystemsandshows a lowerdegreeof linearity.

Cloud liquid water(not shown here)producesa distribution that is very similar to thatof liquid precipitation.Cloudcover, however, (Figure4) representsa convolution of therain,snow andcloudwaterdistributionswitha goodlinearity wheresnow exists at high altitudesandfor theweaker systemsin the presenceof rain. Thesecondarymaximumfor intensesystemsis evidentbut log10 � 1 F � mainly remainsbelow 10� 6.

If the linearity test is appliedto the entireobservation operatorthat is moist physicsparameterizationsandmultiple scatteringradiative transfermodel,thesensitivity of radianceobservablesto realisticperturbationsinthecontrolvectorcanbetested.This canhelpto selectchannelswhicharelessaffectedby non-linearitiesandto developscreeningproceduresfor theexclusionof situationsin which theoperatorcanbeexpectedto behavenon-linearly. Figure5 shows theresultsbasedon thesamedatasetasusedfor Figure2-4 for thesevenSSM/Ichannels.For clarity, only valuesof λ � 10� 10 � 10� 6 � 10� 2 areshown. Theresultsfor λ � 2 andλ � 10arequitesimilar for mostchannels.This indicatesthe limitation of calculatinglog10 � 1 F � by thenumericalaccuracy for smallλ . In mostcases,thebulk of theprobabilitydistribution of log10 � 1 F � remainsbelow 0.Evenfor λ � 1 (not shown), themaximumof thedistributionsis near 2 thatcorrespondsto a 1% differencebetweenfinite-differenceandtangent-linearcalculations.For λ � 2 andλ � 6 two differentregimescanbe identified that refer to the two regimesseenin Figures2-4. Among the SSM/I channels,37v, 37h, 85v,



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Figure5: Frequencydistribution of linearity testparameterfor differentscalingfactors λ andchannels19v(a), 19h(b),22v(c), 37v(d), 37h(e),85v, (f), and85h(g), respectively.



and85h show slightly larger log10 < 1 = F < -valuesthanthe others. This wasalreadyshown in an independentinvestigationsof microwave radiative transfermodelinglinearity (Baueret al. 2006b).

3 Results

3.1 Processing

Theprocessingof rain affectedSSM/I TB’s involvesseveral stepsthatarealsoillustratedin Figure1. Theseincludea datascreeningprior to the1D-Var retrieval, a correctionof systematicdifferencesbetweenobservedandsimulatedTB’s (’bias correction’),a post-retrieval datascreening,anda datathinning. Biascorrectionisa sensitive issuebecauseit representsan areaof trade-off betweentrue instrumentbiasesandmodelbiasesthat can be correctedin the analysis. However, the variationalretrieval framework is definedfor unbiaseddeparturesand,secondly, if systematicincrementsareintroducedinto the analysisunwantedeffectssuchasexcessive precipitationrelease(andsubsequentspin-down) mayoccur.

TheSSM/Iobservationssuffer from ascan-positiondependentbiasthatis causedby thepartialintrusionby thesatellitestructuremainly neartheendof thescan(ColtonandPoe1999,their Figure3). Thesebiasesamountto severaldegreesK andthey arestatic,which meansthat constantbiascorrectionsperscanpositionsuffice.Thesebiaseshave beencalculatedfrom 3 monthsof SSM/I data(F-13, F-14, F-15) over oceans.A cloudcheckwasappliedandthedifferencesof clear-sky TBsbetweenscan-centerandtheotherbeampositionswereaveragedover theentiredataset.Thesebiaseswerederivedfrom observationsaloneto avoid a contaminationof thebiascalculationby scan-angledependentmodelbiasesproducedby, for example,seasurfaceemissivitymodelbiasesasa functionof relative azimuthbetweenscanangleandwind direction.

Thenext processingstageis thedatapre-screeningthatincludesa landsurfaceandsea-icecheck,theexclusionof caseswith highnear-surfacewindspeeds(seeSection3d),acheckfor valid TB observationsandthescreen-ing of clear-sky observationsnot to betreatedin theretrieval. Ideally, the1D-Var retrieval would beappliedinall casesexceptwhereneitherobservationsnormodelfirst-guessfieldsshow cloudsor precipitation.However,theECMWFdataassimilationsystememploysascreeningthatis purelybasedontheobservationssothatcloudandprecipitationscreeningfor clear-sky observationsdoesnot rely on modelfields. This maychangein thefuturewhencloud-affectedobservationswill entertheanalysisat leastaspassive variablesinsidetheobserva-tion operatorto avoid aliasingof thesensitivity to cloudvariablesinto thetemperatureandmoistureanalysis.In ourcase,acheckfor cloudliquid waterandprecipitationpresenceis appliedthatis basedonTB-thresholds.

Oncecloudsand/orrainhavebeenidentified,theobservationoperatoris appliedto themodelfirst-guessprofilesandSSM/I TB’s, i.e. H > xb ? , arecalculated.Notethat theentirescreeningandretrieval procedureis activatedalongthefirst modeltrajectoryat full resolution.This is becausethe1D-Var observation operatorrequiresalargenumberof fieldsthataremostoptimallyaccessedimmediatelyafterthecalculationof themodelphysics.This implementationrequiresthat theobservationsaremappedto themodelgrid (40 km sampling)andto theactualtime step(15 minutewindow). Despitethe channeldependentspatialresolutionof SSM/I footprints,no adjustmentis madeandmodelresolutionandobservationresolutionareconsideredidentical.Theimplica-tionsof this assumptionarepresentedby Baueret al. (2006b). After thecalculationof thefirst-guessmodelequivalentTB’s,afirst-guessdeparturecheckis applied.

The bias correctionusesa single predictor from the model first-guessfields in a linear regression,namelyTCWV. This choiceis reasonablebecausea parameterrelatedto humidity is requiredthat is availablein bothclearandcloudy situationsandfor which the TB’s show sufficient sensitivity. Coefficients, (slopea, offsetb), of the linear fit were calculatedover increasingdatavolumesin September2004 to ensurethat the fit



Figure6: Time-series(expressedasincreasingsamplesize’n’) of gradientsfor bias-correctioncoefficient(a, b; Septem-ber2004)adjustmentin % for channels19v(a), 19h(b), 22v(c), 37v(d), 37h(e),85v, (f), and85h(g), respectively.



Figure 7: TB-departuresbetweenobservationsandbias-correctedfirst-guessmodelvalues(solid), analysisvalues(dot-ted) and uncorrectedfirst-guessmodelvalues(dashed).Left panelsshowdistributionsfor cloud and rain simulations,right panelsshowclear-sky distributionsfor channels19v (a), 19h (b), 22v (c), 37v (d), 37h (e), 85v, (f), and 85h (g),respectively.



Table2: First-guessandanalysisdeparturestatistics(in K) fromclear-sky andrain affectedSSM/Iradianceassimilation(n: samplesize, ∆FG: meanfirst-guessdeparture, σFG: first-guessdeparture standard deviation, ∆AN: meananalysisdeparture, σAN: analysisdeparturestandard deviation).

19v 19h 22v 37v 37h 85v 85hClear-sky:n 221,202 220,966 220,944 221,358 220,690 220,976 219,895∆FG 0.21 0.41 0.33 0.14 0.26 0.13 0.48σFG 1.76 3.01 2.67 1.57 3.13 2.06 4.57∆AN 0.17 0.37 0.25 0.11 0.26 0.12 0.45σAN 1.28 2.03 1.83 1.24 2.39 1.71 3.54Clouds/rain:n 1,472,320 1,472,320 1,472,320 1,472,320 1,472,320 1,472,320 1,472,320∆FG 0.30 0.34 0.17 0.30 0.50 -0.04 0.23σFG 4.05 7.48 3.46 6.22 13.02 5.78 12.67∆AN 0.18 0.10 -0.04 0.16 0.14 -0.04 -0.38σAN 0.92 1.81 0.93 2.87 5.74 4.82 8.85

stabilizes. Figure6 shows the time seriesof the gradientsof thesecoefficientswith increasingdatavolumefor eachchannel,respectively. Thex-axisdenotessamplesizeinsteadof time andtheaxisrangerefersto theentiremonth.For mostchannels,thegradientreducesfairly quickly to lessthan0.1-1%after2-3 weeks.Theimplementedcoefficientshave beentakenthereforefrom thefinal calculationat theendof theperiod.

Figure7 andTable2 show the resultingfirst-guessandanalysisdeparturestatistics.For comparison,similarstatisticshave beengeneratedfrom the clear-sky SSM/I radianceassimilationin the ECMWF analysis.Themeanfirst-guessdeparturesshow thattheremainingradiancebiasesafterapplyingthebiascorrectionareverysimilar for both clear-sky and rain assimilationdata. The first-guessdeparturestandarddeviations of rainaffectedradiancesarebetween1.3-2.8timeslarger thanthosein clearskies. This result is quite remarkablekeepingin mind that the first-guessfields insideprecipitationare expectedto be lessaccuratethan outsideandthat the observation operatoris morecomplex thanthe clear-sky radiative transfermodel. The analysisdeparturesaresmallerby 50%thanthefirst-guessdeparturesin clearconditions,this reductioninsidecloudsandprecipitationamountsto 30%.Thisshows thegoodconvergenceof theminimizationin eithercaseandtheimpactof therespective observationerrordefinition(seenext section).

Figure7 shows, however, thatthebias-correctionworkssuccessfullyonly for thelower threeSSM/I channels.Obviously, the correctionhasto be constrainedfurther for the otherchannels.Adding anotherdegreein thepolynominalfit doesnotfully correctthesebiasesanddoesnotalleviatethenon-Gaussianshapeof thedeparturecurvesfor theupperchannels.Therefore,only thelower threechannelswereconsideredin thefurtheranalysiswhile the other four channelsweremaintainedactive in the 1D-Var retrieval for diagnosticpurposes.Theirobservationerrorsweresetto 999K to eliminatetheir impact.As shown in Figure1, the1D-Var algorithmisthenappliedandemploys bothforwardandadjointof theobservationoperatorin aniterative minimizationofthecost-functionin Equation(1). After minimization,thepost-processingis carriedout. Detailsof the1D-Varperformanceandthepost-processingaredescribedin thenext section.



3.2 Err or definition

Theminimizationis constrainedby bothbackgroundandobservationplusmodelingerrorcovariancematricesB andR. B is specifiedfrom theshort-rangeforecasterrorsof temperatureandspecifichumiditybecausetheseparametersalsoconstitutethe control vector in the 1D-Var retrieval. The forecasterrorsarecalculatedat aratherlow spatialresolutionthat correspondsto a wavenumbertruncationof 95, i.e. about200 km (Rabieret al. 1998)andtheverticalerrorcovariancematrix is constant.Thespatialvariability of B is thereforeonlyintroducedby the error standarddeviation andis supposedto be representative for both clear-sky andcloudscenes.

Part II of thispaper(Baueret al. 2006a)performsa moredetailedstudyof backgrounderrorcovarianceinsidevs. outsideprecipitation.For this, themeandifferencebetween24-hourand48-hourforecastsof temperatureandspecifichumidity for thesametarget time werecarriedout assumingthat short-rangeforecasterrorscanberepresentedby differencesbetweenforecastsover differentperiods.Theresultsindicatethat thecurrentlyavailablestatisticsdo not allow a precipitationspecificerrorformulation.Only dedicatedvalidationprogramswill allow to produceerrorstatisticsfrom independentobservations.

Hollingsworth andLonnberg (1986)establisheda techniquefor theseparationof backgrounderrorsandobser-vationerrorsusingbackgrounddeparturestatisticsover areaswith denselysampledground-basedobservationnetworks.Themethodis basedontheassumptionthatobservationerrorsarespatiallyuncorrelatedwhile back-grounderrorsarespatiallycorrelated.Therefore,plotting covariancesof backgrounddeparturesfrom differentpointsagainsttheir separationdistancecanbeusedto distinguishbetweennon-zerocovariancesfor separationdistancesd @ 0 (betweenobservations)solelydueto thebackgroundtermandthosedueto bothbackgroundandobservationtermsatd A 0. Figure8 shows theresultfor all sevenSSM/I channelsusing116,569samples.Its is assumedthatatd A 0 thevarianceof backgrounddeparturesσ2

FG A σ2B B σ2

R with σ2B beingexpressedasa

variancein radianceunits.Thebackgroundterm,σ2B, canthenbeobtainedfrom extrapolatingthehistogramfor

d @ 0 to d A 0. This seemsjustifiedbecausetheshapeof thehistogramis rathersmoothandflattenstowardsd A 0. Theresultingerrortermsaresummarizedin Table3.

Theobservationerrorsareslightly largerthanthebackgrounderrorsandlargerfor horizontallypolarizedchan-nelsthanfor vertically polarizedchannels.The latter is explainedby the larger dynamicrangeof the signalat horizontalpolarization.This alsomeansthat the observation errorsaremainly a resultof modelingerrorsbecausethe radiometricnoiseis similar for all channels(between0.5 and1 K) while themodelingerrorwilldependon themagnitudeof thesimulatedsignal. This raisesthequestionif theHollingsworth andLonnbergtechniquecanbe appliedherebecausethe observation errorsmustbe spatiallyuncorrelated.This mustalsoapplyto themodelingerrorsbecausethebackgrounddeparturesareobtainedfrom yo = H > x ? . While yo is mostlikely uncorrelated,H > x ? maybenot. This alsoholdsfor theinter-channelcorrelationthatmaybeintroducedby errorsin H. However, Moreauetal. (2003)haveshown thatincludingnon-zerooff-diagonalelementsin σRdoesnot significantlyaffect the1D-Var performance.

As an alternative solution,thebackgrounderrorscould be calculatedfrom the diagonaltermsof HBH T thatis the translationof theoperationalmodelbackgrounderrorcovariancematrix into observation spaceandbyapplyingσ2

R A σ2FG = σ2

B. However, this would alsointroducemodelingerrorsinto HBH T andneitherwouldproducea cleanseparationof error contributions. Figure9 shows the result from this calculationthat is thesquarerootof thediagonaltermsof theHBH T matrix for eachSSM/Ichannel.Theleft panelsdenotesituationswhereonly the large-scalecondensationschemewasactive in the1D-Var minimizationwhile theboth large-scalecondensationandconvectionschemeswereactive in thedatareproducedin theright panels.Bothmedian(dottedline) andmode(dashedline) of thedistributionsareoverplottedandtheir valuesaregiven in Table3.Sincethedistributionsareratherwide, thevalueswereroundedoff to integernumbers.



Figure 8: Spatialcovarianceof SSM/ITB’s for channels19v(a), 19h(b), 22v(c), 37v(d), 37h(e), 85v, (f), and85h(g),respectively, asa functionof separationdistanced (in km) from116,569observations.



Figure9: Backgrounderror standard deviationexpressedin radiancetermsfor channels19v(a), 19h(b), 22v(c), 37v(d),37h(e),85v, (f), and85h(g), respectively, from116,569observations.Left (right) panelsrepresentcaseswith large-scalecondensation(+ convection)physicsparameterizationschemesactivated.



Table3: Estimationof backgroundandobservationerror standard deviations(in K) fromthespatialcovarianceof back-grounddepartures(HollingsworthandLonnberg 1986)basedon116,569observations.Medianandmodeof backgrounderror distributionsin radiancespacefrom HBHT calculationsfor caseswith activelarge-scalecondensation(LS) andconvection(CV)schemes.

19v 19h 22v 37v 37h 85v 85hσB 2.2 4.1 2.0 3.5 7.4 2.8 7.7σR 2.8 5.2 2.5 4.4 9.0 4.0 8.4Median:σHBHT C LS 5 10 7 8 14 7 16Median:σHBHT C LS B CV 21 30 18 27 25 12 22Mode: σHBHT C LS 5 8 6 5 10 5 12Mode: σHBHT C LS B CV 20 37 7 8 22 4 16

Themagnitudeof backgroundandobservationerrorsobtainedfrom theHollingsworth-Lonnberg methodwererathersimilar and by a factor of 2-3 smaller than thoseobtainedfrom the HBH T-calculations. The mainexplanationfor this is that the forward calculationsusing backgroundprofiles of temperatureandmoistureproduceradiancesthat arecloseto the observationswhile the calculationof backgroundvariancepropertiesin radiancespaceis not closeto theobservedminusmodelledvariance.This would suggestthat theB-matrixin cloudsandprecipitationcontainstoo largecovariances.Thecaseswhereonly the large-scalecondensationschemeis active show much lower valuesfor the medianand modeof the distributions comparedto thosewherealsoconvectionis found. Whenconvectionis active the atmosphereis likely to be moreunstableandthusthe combinedsensitivity of large-scalecondensationandconvectionschemeincreases.The convectionschemeproducesdetrainedwaterthatamplifiesprecipitationgenerationin theconvectionscheme.Secondly,convectionis generallymoreactive in theTropicswherealsoB for specifichumidity is larger.

Both backgroundandobservation errorsaredifficult to specify in cloud andrain affectedareas.At present,no operationalweatherforecastingsystemhasanexplicit formulationof modelerrorsfor thesecasesso thatindirectmethodssuchastheHollingsworth andLonnberg techniquerepresenttheonly alternative. Moreover,the retrieved errorsobtainedfrom this methodseemrealisticandprovide a balancebetweenbackgroundandobservation errorsgiven the calculatedbackgrounddepartures.The discrepancy betweenthe resultsfor thebackgrounderrorsin radiancetermsobtainedfrom the Hollingsworth-Lonnberg andthe HBH T-methodalsosuggestthat thereis a needfor a betterdescriptionof moisturebackgrounderrorsinsidecloudsandprecipita-tion.

3.3 Convergence

Figures10aand10b show an exampleof the averagereductionof both cost function and its gradientfor a12-houranalysisfor 70,149samples.In the currentimplementation,a maximumnumberof iterations,k, of19 is allowed, otherwise,no convergenceis assumed.Figure10cshows thatmostretrievals requirebetween5 and15 iterations.Thecost-functiongradientsarereducedby 4 (2) ordersof magnitudefor theobservation(background)components,respectively. Thissuggestastableperformance.

A zonalcross-sectionsof theproportionbetweensuccessful1D-Var retrievalsandscreenedretrievalsis shownin Figure11afor thefirst 20daysin January2005with 5 degreeresolution.Thefractionof successfulretrievalsexhibits lowernumbersin theWinterhemisphere.Thisreductionis mainlydueto theincreaseof rejectionsdueto excessive TCWV increments,i.e., thedifferencebetweenTCWV retrievalsandthemodelfirst-guessvalues.A thresholdof 20%with respectto thefirst-guessTCWV waschosento avoid excessivemoisturechangeswithpossiblynegative impactdueto themoistphysicalparameterizationperformance.



The areaswith TCWV incrementrejectionsare mainly locatedin the regions of frontal overpassesin theNorthernoceans. In theseregions, sea-surfacetemperaturesare ratherlow andmost of the precipitationisfrozen.Generally, thethreechosenSSM/I channelsshow little to no sensitivity to frozenprecipitationsothattheTCWV retrievalsuselittle informationfrom theobservations.

Thedistribution of retrieval rejectionsdueto non-convergenceshows higherrejectionratesin dry sub-tropicalareas.This rejectionis activatedduring the minimizationif incrementslarger than10 timesthe backgrounderrorstandarddeviation appearor if negative moisturesor unrealistictemperaturesareproduced.Again, thisrejectionflag preventsthe moist physicalparameterizationschemesfrom failing. As expected,the averagenumberof 1D-Var iterations(Figure11b) follows thedistribution of rejectionsdueto convergenceproblems.The relative TCWV increments,∆TCWV, in Figure 11b show a zonally symmetricdistribution due to thescreeningof excessive incrementsdescribedearlier. However, the zonal structurereveals that the averageincrementsarepositive (about1%) andthatthey areslightly larger in theSubtropics.This is in contrastto theresultof Marecaletal. (2002)whoidentifiedanegativeaverageTCWV incrementfrom theassimilationof TMIrain rateestimates.Dependingon the rainfall retrieval algorithm,Marecalet al. foundan averageincrementof = 0 D 1kgmE 2. Our resultof 1% translateto about0 D 3kgmE 2. This meandepartureis reducedin the4D-Varanalysisto about0 D 04kgmE 2 (Baueret al. 2006a).Therearemany potentialexplanationsfor this difference,namelythe approachof assimilatingrain ratesvs. TB’s and the different moist physicalparameterizationsschemesusedin the1D-Varalgorithmsaswell theevolutionof thenon-linearmodelphysicalparameterizations.AnotherreasoncouldbethatMarecalet al. did notapplyabias-correctionto theretrievedrain rates.

3.4 Impact

Figure 12 shows a mid-latitude front over the North Atlantic on December31, 2004 from the analysisat00 UTC. Figure 12a displaysthe differencebetweenthe 19v and 19h SSM/I channelsthat is indicative ofincreasingprecipitationintensity with decreasingpolarizationdifference. The polarizationis producedbysurfaceemissionandhasa maximumin clearskies.With increasingopticaldepthdueto radianceabsorptionandmultiplescatteringfromhydrometeors,thepolarizationsignalis obscured.Sincethepolarizationdifferenceonly decreasesto about30 K, thetotal condensedwateramountis not very large.

TCWV incrementsfrom 1D-Var retrievalsareoverlayedandshow large-scale(up to 30%)positive incrementsin thepost-frontalcloudbandsweakernegative incrementsaheadof thefront while thecloudbandsthemselvesareonly locally modified. The meanprofile incrementssuggestthat positive TCWV incrementsaremainlyproducedby an increaseof moisturebelow modellevels50 ( F 900hPa) anda temperaturedecreasebetweenmodel levels 43 and58 ( F 650 and1000hPa). However, the profile incrementstandarddeviationsarelargeindicatinga substantialspatialvariability. Liquid precipitationonly increasesnearthe surfacewith a strongimpacton frozenprecipitationsincethe largestincrementsarelocatedin the cold sectorof the disturbance.Cloud liquid waterandcloud cover arenearlyunchanged.As previously mentioned,the threeactive SSM/Ichannelsmainly respondto changesin liquid waterandrain but thestrongestimpactis observed throughthemoistphysicalparameterizationson frozenprecipitation.

Thesecondexample(Figure13)originatesfrom thesameanalysisandshowsatropicaldisturbance(’Chambo’)in theSouthernIndianOceanpassingby theislandsof La ReunionandMauritius.Thepolarizationdifferencesarestill larger than20 K suggestingthat thesystemis not fully developed.Therelative 1D-Var TCWV incre-mentsaremuchsmallerthanin themid-latitudecasesthat is lessthan15%. Keepingin mind tropicalTCWVamounts,10%in relativeincrementsrepresentquitesubstantialabsoluteincrements.Theincrementsaremainlypositive in thesystem’s rain bandsandnegative in the lessintenseareas.This indicatesan overestimationofrain coveragein the first guess.The profilesof incrementsshow warminganddrying (Figure13b,c) over adeeplayer betweensurfaceand750 hPa. Above the freezinglevel, both liquid and frozenprecipitationare



Figure10: Meanandstandard deviationsof normalized1D-Var cost-function,J G , for observation(solid)andbackground(dashed)terms(a); gradientof cost-function(b), respectively, as a functionof iteration number, k. Distribution of fre-quencyof occurrenceof 1D-Var iterations(c)



Figure 11: Zonaldistribution of percentageof successful1D-Var retrievals(white),too large TCWVanalysisdepartures(light grey), too large TB analysisdepartures(dark grey) and convergencefailures(black) for January1-20, 2005(a).Zonaldistribution of mean1D-Var iterationnumber(white)andmeanrelativeTCWVincrement(in %; light grey) (b).

slightly enhancedbut rain is reducedbelow. Cloud liquid waterandcloudcoveragerespondsimilarly in bothcaseswith incrementsof thesamesignalongtheprofile.

Global incrementstatisticsfrom theentiremonthof September2004aresummarizedin Figure14 for TCWV(a), large-scale(b) and convective (c) precipitation,respectively. The F 0.5% increasein TCWV from as-similatingSSM/I TB’s is reflectedin the frequency distribution andpropagatesinto thosefor both stratiformandconvective precipitation.For precipitation,the incrementsaredisplayedasdBR that is 10log10∆wR with∆wR A wRH AN = wRH FG. This is because,globally, precipitationfollows a ratherlog-normaldistribution.

The geographicaldistribution of relative incrementsis displayedin Figure15. Thereare regionswith veryspecificpositive andnegative TCWV increments(Figure15a),respectively. Subtropicalareaswith lower rainintensitiesreceive largepositive relative TCWV incrementswith little effect on precipitation.Very smallneg-ative TCWV incrementsin theNorthernoceansproducea significantreductionof large-scaleandsometimesconvective precipitation. In the SouthernIndian Ocean,the strongestpositive precipitationincrementsareproducedwhile the strongestnegative onesoccurin the SouthernPacific. The areasof large convective rain



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Figure 14: Frequencydistribution of TCWV(a; in %), stratiform precipitationflux (b; in dBR)andconvectiveprecipita-tion flux (b; in dBR)incrementsfrom1D-Var retrievalsin September2004.



Figure 15: Global incrementdistribution of TCWV(a; in %), stratiform precipitationflux (b; in dBR) and convectiveprecipitationflux (b; in dBR)from1D-Var retrievalsin September2004averagedto 2.5o resolution.



incrementscorrespondto only a few casespermonthandto situationsin which thefirst-guessconvective rainrateis very small. Therefore,incrementsof, for example,10 dB that is oneorderof magnitudestill produceweakrain intensities.

Generally, the large-scalecondensationschemeincrementsaresmootherandcover theentireglobe. Most ofthetime, theareasof positive andnegative TCWV incrementsdirectly translateinto incrementsof large-scaleprecipitationof thecorrespondingsign.This is becauseof thehighersensitivity of thelarge-scaleprecipitationparameterizationto moisturechangescomparedto theconvectionschemebecausetheair is alreadysaturatedinthepresenceof large-scalecondensation..Thelargestrain incrementsoccurin areaswith little rain sothattheglobal impactof therain assimilationis ratherweak(seealsoFigure14). Local incrementscanbelargeevenin thepresenceof significantamountsof rain, for examplein theCaribbeanSeaandnearmid-latitudefrontalsystems.How muchof this impactremainsin the4D-Var analysisandhow this will affect themedium-rangeforecastswill beshown in thesubsequentpaperby Baueretal. (2006b).

4 Discussion

This paperis the first part of the descriptionof methodologyandresultsof the assimilationof rain affectedSSM/I radiancesat ECMWF. Basedon previous studies,a 1D+4D-Var approachwaschosenwherethe radi-ancesareusedasobservationsin a1D-Var retrieval of total columnwatervapourthatis thenassimilatedin the4D-Var system.Themaindevelopmentin thefirst stageis theobservationoperatorthatconsistsof linearizedconvectionandlarge-scalecondensationschemesaswell asa multiplescatteringradiative transfermodel.

Even thoughthe 1D-Var retrieval employs a non-linearminimizationalgorithm,the linearity of the observa-tion operatorhadto be evaluatedbecauseit determinesthe quality of the convergence. The linearity of themoistphysicsparameterizationsandtheradiative transfermodelwereinvestigatedseparatelyfor realisticper-turbationsdeducedfrom analysisincrementsthatwereobtainedfrom the1D-Varretrieval itself. Only for ratherintenserainevents,thelinearityseemeddeterioratedbut evenfor mostof thesituations,thedifferencesbetweenfinite-differenceandtangent-linearcalculationsremainedwithin the10%level. The linearity performanceoftheentireoperatorwasfound to be betterthanfor the microphysicsparameterizationsalonethat showed theweakeststatisticsfor frozenprecipitation.Thedependenceon SSM/I channelwasfoundto beratherweak.

A screeningandbiascorrectionprocedurewasintroducedthat reducestheanalysesto thosecaseswherethe1D-Varretrieval canbeexpectedto performwell andanintroductionof TCWV biasesinto the4D-Varanalysisis therebyavoided.Comparedto thedeparturestatisticsof SSM/I radiancesin clearskies,therainobservationoperatorperformsextremelywell for thelowestthreeSSM/I frequencies.Radiancedeparturestandarddevia-tionsarelessthana factorof 3 larger thanthosein clearskies.This is a very goodresultgiventhecomplexityof theobservationoperator.

TheHollingsworth-Lonnberg methodfor the separationof backgroundandobservation errorstandarddevia-tionswasimplemented.This indirectalgorithmprovidedrealisticresultsandproducedbalancederrorvaluesfor all SSM/I channels.A direct observation error estimationis not possiblebecausethe largestcontributioncanbeattributedto theobservationoperatorfor whichno independentvalidationexists.

The1D-Varconvergenceperformancewasanalyzedfor a three-weekperiodin January2005insidethecurrentoperationalsystem. The numberof minimization failuresis below 5% andmost datarejectionsaredue toTCWV incrementsthat wereconsideredtoo large. The associatedthresholdswill have to be refinedin thecontext of the4D-Var analyses.Examplesof 1D-Var incrementstatisticswereshown in a mid-latitudefrontalsystemanda weaktropical cyclone. Globally, theTCWV andprecipitationincrementswerepositive for thechosenanalysisdate.This moisteningof theatmospherewasexpressedasanincreasein both large-scaleand



convective precipitation.A slight dependenceon latitudewasidentifiedwith maximaaround ¢ 40 degreesoflatitudein ratherdry areas.Thegeographicaldistribution of large-scaleandconvective rain incrementsshowedseveraldistinctfeatures.Thelarge-scaleschemehasastrongersensitivity to moisturechangesandis activatedalmosteverywhere.Outsidethe tropics,the convectionschemeshows large incrementsin areaswherelittlerain is present.

In summary, theimplemented1D-Varmethodologyperformedverywell with thechosenobservationoperator.Microwave radiancesaremainly sensitive to integratedhydrometeorcontentsandalwaysshow sensitivity toTCWV andto a lesserdegreeto atmospherictemperature.Therefore,evenin theabsenceof backgroundpre-cipitationa minimizationcanbeperformedduringwhich cloudsand/orprecipitationaregenerated.Theerrordistributionsarevery smoothand,at leastfor the lower frequencies,show near-Gaussianshapeswith reason-ableerrorvalues.Part II of this paperwill investigatetheimpactof TCWV pseudo-observationsproducedbythe 1D-Var retrieval on the 4D-Var analysesand forecasts.This is a new observation type in areasthat areusuallyscreenedout in satellitedataanalyses.Theassimilationof rain affectedradiancesthereforehasa largepotentialfor futureforecastimprovementsbut theimpactwill greatlydependon theassimilationsystemitselfandtheinteractionbetweenmoisture-relatedobservationsandmodeldynamicsprescribedby theassimilationsystemandby theformulationof backgrounderrorcovariancestatistics.

Acknowledgements

The authorsaregrateful to Jean-Noel Thepautfor many valuablediscussionson the subjectand to MarineBonazzolafor technicalsupport. The work waspartly fundedby the EuropeanSpaceAgency (ESA) undercontractNo. 17193/03/NL/GS.

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